Trace the curve of the trajectory of a cannonball fired at an angle of 30∘ to the horizontal. Neglect the effect of air resistance. Also, calculate the maximum height and horizontal distance (range) attained by the cannonball.
To calculate the trajectory, we will use the equations for projectile motion. The key variables are:
The formula for the maximum height attained by a projectile is:
Substituting θ=30∘ and g=9.81m/s2:
Therefore, the maximum height is:
The formula for the range (horizontal distance) is:
Substituting θ=30∘ and g=9.81m/s2:
The horizontal and vertical positions as a function of time are given by the parametric equations: